Question: Simplify the following expression: $n = \dfrac{-3r^2 - 51r - 216}{r + 8} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ n =\dfrac{-3(r^2 + 17r + 72)}{r + 8} $ Then we factor the remaining polynomial: $r^2 + {17}r + {72} $ ${8} + {9} = {17}$ ${8} \times {9} = {72}$ $ (r + {8}) (r + {9}) $ This gives us a factored expression: $\dfrac{-3(r + {8}) (r + {9})}{r + 8}$ We can divide the numerator and denominator by $(r - 8)$ on condition that $r \neq -8$ Therefore $n = -3(r + 9); r \neq -8$